`lim_(x->o)(e^x-1)/(e^(2x)-1)`

lim_(x->0)(e^(5x) - 1)/(3x)

Evaluate lim_(xto0) (e^(x)-1-x)/(x^(2)).

Solve lim_(x->oo)(e^x-e^-x)/(e^x-e^-x)

lim_(x->e) (lnx-1)/(x-e)

Show that lim_(xto0) (e^(1//x)-1)/(e^(1//x)+1) does not exist.

Statement 1: If lim_(xto0){f(x)+(sinx)/x} does not exist then lim_(xto0)f(x) does not exist. Statement 2: lim_(xto0)((e^(1//x)-1)/(e^(1//x)+1)) does not exist.

Evaluate: (lim)_(x->e)(logx-1)/(x-e)

Evaluate lim_(xto1) (x^(2)+xlog_(e)x-log_(e)x-1)/((x^(2))-1)

lim_(x->0) (2e^sinx-e^(-sinx)-1)/(x^2+2x)

lim_(xto0)((e^(x)-1)/x)^(1//x)